Growth of fractal structures in fullerene solutions

Abstract

The phenomenon of formation of fractal cluster structures in fullerene solutions discovered in recent experiments is analyzed theoretically. As the basis for analysis the standard fractal cluster growth approach is used. The simplest approximation based on the supposed temporal independence of both fractal cluster dimensionality and attachment probability of two clusters does not provide agreement between the measured and calculated cluster growth data. A satisfactory agreement is attainable in a frame of the Reaction Limited Cluster Aggregation model in the supposition that the attachment probability γ depends on cluster size. The best fitting is obtained for the dependence γ = γ0(r0/R)α, where γ0 = 10−7, α = 2. The possible physical mechanism clarifying such a dependence is considered.